This invention relates to the processing of geophysical data in order to render it more useful in interpreting the geophysical characteristics of the earth in the exploration for oil and gas deposits. More specifically, this invention relates to a method of processing seismic traces to accurately estimate the amplitude and phase spectrums of the seismic wavelet and then proceed to modify that wavelet into an output wavelet having the desirable features of zero phase and low sidelobe level for maximum resolution and dynamic range. Such output wavelet has been shown useful in analyzing the characteristics of the geological formation under investigation. Further, while the invention will be described with respect to the processing of seismic data, it is equally applicable to other types of geophysical data, such as well logs, gravity information, and magnetic data.
In seismic exploration, data is obtained by first creating an artificial disturbance along the earth by use of dynamite or the like. The resulting acoustic waves travel downwardly in the earth and are reflected upward from subsurface reflecting interfaces. The reflected waves are received at detectors (geophones or hydrophones) located along the surface and recorded in a reproducible form. Ideally, the waves recorded at the detectors would be exactly representative of the reflecting characteristics (referred to as the reflectivity function) of the earth without any undesirable components, such as noise or distortion.
Unfortunately, the signals recorded at the detectors contain many undesirable components which often obscure the reflectivity function of the earth and prevent the finding of an area of the earth where oil and gas deposits may be present. One undesirable component of the recorded seismic data is due to the seismic disturbance created by the explosion of dynamite and known as the shot pulse. Ideally, the time waveform of the shot pulse should be a simple short pulse, such as an impulse or a square wave. Instead, the shot pulse resulting from the explosion of dynamite, or almost any other known seismic source, is a complex train of wavelets. As a result, the reflectivity function of the earth is obscured by the complex waveforms of the reflected shot pulse appearing on the recorded data. To make matters worse, the shot pulse changes in amplitude and shape with depth in the earth so that the recorded data contains reflections of a time-varying shot pulse. Other undesirable components in the seismogram may be referred to collectively as the distortion operator. These include the effect of multiple reflections, ghosts, reverberations, and other types of distortion known in the seismic art. Furthermore, the effect of the distortion operator is intermixed in a complex way with the shot pulse. Therefore, the distortion operator and the shot pulse may be lumped together as a single component and called the distorted shot pulse, or seismic wavelet. It is desirable to remove the effects of the distorted shot pulse on the seismogram, but the difficulty is that the waveform of the distorted shot pulse is unknown.
The traditional method of deconvolution, generally known as "flat-iron" or Wiener-Levinson deconvolution method, assumes that the seismic wavelet is minimum phase or "front-loaded". It is also assumed the reflectivity function is white (i.e. its amplitude spectrum is constant with frequency.) Under these assumptions, the amplitude spectrum of the wavelet and the amplitude spectrum of the seismic trace are equivalent. Further, once the amplitude spectrum is determined, the phase spectrum can be easily calculated by using the above-mentioned assumption that the wavelet is minimum phase after sampling. Once the seismic wavelet is estimated from the calculated amplitude spectrum and phase spectrum, an inverse filter can be designed to compress the seismic wavelet into a short output wavelet close to a spike. In the actual implementation of the Wiener-Levinson method, the inverse filter is calculated in one step from the autocorrelation of the seismic trace. Since the filter calculated in the Wiener-Levinson method is minimum phase, the output wavelet tends to be minimum phase, instead of zero phase. It is the purpose of this invention to improve upon the results of the prior art deconvolution method by providing better phase compensation than Wiener-Levinson deconvolution and thus produce a zero phase output wavelet. In contrast to prior methods, this invention assumes that the analog seismic wavelet is minimum phase but recognizes that the minimum-phase property is not necessarily preserved after sampling. This invention also avoids errors in the phase estimate of the wavelet by prior art methods caused by noise. Such noise is either actually present on the seismic trace, or artificially introduced to stabilize filter design.
A method of processing geophysical data which improved upon the above-described method was disclosed in U.S. Pat. No. 3,396,365, issued to Clyde W. Kerns for a method of processing geophysical data with stable inverse filters. Kerns discloses a method of processing seismic data to suppress coherent noise such as multiples, reverberations and ghosts. In Kerns, an autocorrelation function is produced from an input seismic signal to characterize the noise. A white spike is added to the center point of the autocorrelation function to assure the stability of an inverse filter which is generated from the autocorrelation function. The input seismic signal is then convolved with the inverse filter to produce a filtered signal with the undesired components suppressed.
It should be noted, however, that the use of methods such as those disclosed in Kerns as well as the prior art Wiener-Levinson method typically includes the estimation of seismic wavelet amplitude spectrum by assuming a white reflectivity. One drawback to such an assumption is that any deviation of the reflectivity from whiteness produces a biased (and thus inaccurate) estimate of the amplitude spectrum. Subsequent use of this estimate in deconvolution will result in removing part of the reflectivity information sought in performing the above-described procedure. Therefore, in accordance with this invention, the effects of the nonwhite reflectivity of the earth formation upon the processed wavelet is reduced by averaging the autocorrelation function of the seismic trace over several traces in the shot to thus whiten the reflectivity. In such a manner, this invention improves over both the Wiener-Levinson and Kerns methods.